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104
DOUBLE AFFINE HECKE ALGEBRAS AND BISPECTRAL QUANTUM KNIZHNIKZAMOLODCHIKOV EQUATIONS
, 2008
"... We use the double affine Hecke algebra of type GLN to construct an explicit consistent system of qdifference equations, which we call the bispectral quantum KnizhnikZamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik’s quantum affine KZ equations associated to principal series repre ..."
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Cited by 13 (5 self)
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We use the double affine Hecke algebra of type GLN to construct an explicit consistent system of qdifference equations, which we call the bispectral quantum KnizhnikZamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik’s quantum affine KZ equations associated to principal series
Quantum Knizhnik–Zamolodchikov equation,
, 2005
"... generalized Razumov–Stroganov sum rules and extended Joseph polynomials P. Di Francesco # and P. ZinnJustin ⋆ We prove higher rank analogues of the Razumov–Stroganov sum rule for the groundstate of the O(1) loop model on a semiinfinite cylinder: we show that a weighted sum of components of the gro ..."
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of the groundstate of the Ak−1 IRF model yields integers that generalize the numbers of alternating sign matrices. This is done by constructing minimal polynomial solutions of the level 1 Uq ( sl(k)) quantum Knizhnik–Zamolodchikov equations, which may also be interpreted as quantum incompressible q
Quantum Knizhnik–Zamolodchikov equation,
, 2005
"... generalized Razumov–Stroganov sum rules and extended Joseph polynomials P. Di Francesco # and P. ZinnJustin ⋆ We prove higher rank analogues of the Razumov–Stroganov sum rule for the groundstate of the O(1) loop model on a semiinfinite cylinder: we show that a weighted sum of components of the gro ..."
Abstract
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of the groundstate of the Ak−1 IRF model yields integers that generalize the numbers of alternating sign matrices. This is done by constructing minimal polynomial solutions of the level 1 Uq ( sl(k)) quantum Knizhnik–Zamolodchikov equations, which may also be interpreted as quantum incompressible q
Quantum Knizhnik–Zamolodchikov equation,
, 2006
"... generalized Razumov–Stroganov sum rules and extended Joseph polynomials P. Di Francesco # and P. ZinnJustin ⋆ We prove higher rank analogues of the Razumov–Stroganov sum rule for the groundstate of the O(1) loop model on a semiinfinite cylinder: we show that a weighted sum of components of the gro ..."
Abstract
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of the groundstate of the Ak−1 IRF model yields integers that generalize the numbers of alternating sign matrices. This is done by constructing minimal polynomial solutions of the level 1 Uq ( sl(k)) quantum Knizhnik–Zamolodchikov equations, which may also be interpreted as quantum incompressible q
Quantum Knizhnik–Zamolodchikov equation: reflecting boundary . . .
 J. PHYS. A
, 2007
"... We consider the level 1 solution of quantum Knizhnik–Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley–Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it to the weighted enumeration of Cyclically Symmetric Transpos ..."
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Cited by 50 (15 self)
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We consider the level 1 solution of quantum Knizhnik–Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley–Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it to the weighted enumeration of Cyclically Symmetric
QUANTUM ISOMONODROMIC DEFORMATIONS AND THE KNIZHNIK–ZAMOLODCHIKOV EQUATIONS
, 1994
"... Viewing the Knizhnik–Zamolodchikov equations as multi–time, nonautonomous Shrödinger equations, the transformation to the Heisenberg representation is shown to yield the quantum Schlesinger equations. These are the quantum form of the isomonodromic deformations equations for first order operators ..."
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Cited by 22 (0 self)
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Viewing the Knizhnik–Zamolodchikov equations as multi–time, nonautonomous Shrödinger equations, the transformation to the Heisenberg representation is shown to yield the quantum Schlesinger equations. These are the quantum form of the isomonodromic deformations equations for first order operators
Emptiness Formation Probability and Quantum KnizhnikZamolodchikov Equation
"... We consider the onedimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of formation of a ferromagnetic string P (n) in the antiferromagnetic groundstate. We call it emptiness formation probability [EFP]. We suggest a ..."
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Cited by 18 (11 self)
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new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum KnizhnikZamolodchikov equation [qKZ]. We calculate EFP for n for inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also
Quantum KnizhnikZamolodchikov equations and holomorphic vector bundles
 Duke Math. J
, 1993
"... In 1984 Knizhnik and Zamolodchikov [KZ] studied the matrix elements of intertwining operators between certain representations of affine Lie algebras and found that they satisfy a holonomic system of differential equations which are now called the KnizhnikZamolodchikov (KZ) equations. It turned out ..."
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Cited by 1 (0 self)
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In 1984 Knizhnik and Zamolodchikov [KZ] studied the matrix elements of intertwining operators between certain representations of affine Lie algebras and found that they satisfy a holonomic system of differential equations which are now called the KnizhnikZamolodchikov (KZ) equations. It turned out
Results 1  10
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104